Basic properties
| Modulus: | \(759\) | |
| Conductor: | \(759\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(110\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 759.ba
\(\chi_{759}(26,\cdot)\) \(\chi_{759}(59,\cdot)\) \(\chi_{759}(71,\cdot)\) \(\chi_{759}(104,\cdot)\) \(\chi_{759}(119,\cdot)\) \(\chi_{759}(146,\cdot)\) \(\chi_{759}(170,\cdot)\) \(\chi_{759}(179,\cdot)\) \(\chi_{759}(236,\cdot)\) \(\chi_{759}(257,\cdot)\) \(\chi_{759}(269,\cdot)\) \(\chi_{759}(278,\cdot)\) \(\chi_{759}(284,\cdot)\) \(\chi_{759}(302,\cdot)\) \(\chi_{759}(311,\cdot)\) \(\chi_{759}(317,\cdot)\) \(\chi_{759}(335,\cdot)\) \(\chi_{759}(377,\cdot)\) \(\chi_{759}(416,\cdot)\) \(\chi_{759}(422,\cdot)\) \(\chi_{759}(443,\cdot)\) \(\chi_{759}(449,\cdot)\) \(\chi_{759}(455,\cdot)\) \(\chi_{759}(476,\cdot)\) \(\chi_{759}(509,\cdot)\) \(\chi_{759}(515,\cdot)\) \(\chi_{759}(533,\cdot)\) \(\chi_{759}(542,\cdot)\) \(\chi_{759}(554,\cdot)\) \(\chi_{759}(581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{55})$ |
| Fixed field: | Number field defined by a degree 110 polynomial (not computed) |
Values on generators
\((254,277,166)\) → \((-1,e\left(\frac{1}{5}\right),e\left(\frac{8}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(13\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 759 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{110}\right)\) | \(e\left(\frac{17}{55}\right)\) | \(e\left(\frac{3}{110}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{51}{110}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{21}{55}\right)\) | \(e\left(\frac{41}{110}\right)\) | \(e\left(\frac{34}{55}\right)\) | \(e\left(\frac{43}{110}\right)\) |